Growing Beans ProjectBroad Beans

LECTURER: MS. GRACE

Done by: Faisal, Hussain, Karthik and Faiz

11 - Nov, 2011

BROAD BEAN

Broad bean is a specie of bean native to north Africa and southwest Asia

They are dark brown outside and light yellow inside

They are sweet and soft and easily digested

The most popular use of broad beans in western world is for sprouting. Interestingly, the sprouts contain vitamin C that is not found in the bean

NUTRITIONMature seeds, rawNutrition value per 100 g (3.5 oz)

Energy 1,452 kJ (347 kcal)Carbohydrates 62.62 gSugars 6.60 gDietary fiber 16.3 gFat 1.15 gProtein 23.86 gVitamin C 4.8 mg (8%)Calcium 132 mg (13%)Magnesium 189 mg (51%)Phosphorus 367 mg (52%)Potassium 1246 mg (27%)Sodium 15 mg (1%)

Boiled mung beans

Nutrition value per 100 g (3.5 oz)

Energy 441 kJ (105 kcal)Carbohydrates 19.15 gSugars 2.00 gDietary fiber 7.6 gFat 0.38 gProtein 7.02 gVitamin C 1.0 mg (2%)Calcium 27 mg (3%)Magnesium 0.298 mg (0%)Phosphorus 99 mg (14%)Potassium 266 mg (6%)Sodium 2mg (0%)

WITHOUT FERTILIZER (TABLE)

Days Height (cm)

1 122 173 224 245 246 25.57 268 269 26

10 27

SCATTER PLOT

0

5

10

15

20

25

30

0 2 4 6 8 10 12

Height

Height

LINEAR REGRESSION

y = 1.3667x + 15.433R² = 0.7365

0

5

10

15

20

25

30

35

0 2 4 6 8 10 12

Height

Height

QUADRATIC REGRESSION

y = -0.2879x2 + 4.5333x + 9.1R² = 0.9456

0

5

10

15

20

25

30

0 2 4 6 8 10 12

Height

Height

CUBIC REGRESSION

y = 0.0552x3 - 1.1981x2 + 8.7315x + 4.3667R² = 0.9906

0

5

10

15

20

25

30

0 2 4 6 8 10 12

Height

Height

Poly. (Height )

QUARTIC REGRESSION

y = -0.0028x4 + 0.1161x3 - 1.6438x2 + 9.9495x + 3.4167

R² = 0.9912

0

5

10

15

20

25

30

0 2 4 6 8 10 12

Height

Height

EXPONENTIAL REGRESSION

y = 15.289e0.0691x

R² = 0.6642

0

5

10

15

20

25

30

35

0 2 4 6 8 10 12

Height

Height

LOGARITHMIC REGRESSION

y = 6.3795ln(x) + 13.314R² = 0.9407

0

5

10

15

20

25

30

0 2 4 6 8 10 12

Height

Height

THE BEST FIT MODEL

Model R2

Linear 0.7365

Quadratic 0.9456

Cubic 0.9906

Quartic 0.9912

Exponential 0.6642

Logarithmic 0.9407

The model which fits the best is Quartic Regression

BEST FIT QUARTIC REGRESSION

0 2 4 6 8 10 120

5

10

15

20

25

30

f(x) = − 0.00276807 x⁴ + 0.11606449 x³ − 1.64379371 x² + 9.94949495 x + 3.41666667R² = 0.991162300876723

Height

Height Polynomial (Height )

Y=-0.0028x4 + 0.1161x3 – 1.6438x2 + 9.9495x + 3.4167

Domain : (0,16.7198)

Range : (0,34.0827)

X-intercept : (22.4967,0)

Y-intercept : (0,3.4167)

Properties of the Best fit Function

Predictionsf(11)=27.4957

f(13)=30.0589

f(15)=32.8917

f(16)=33.8407

f(17)=34.0405

f(20)=25.6867

As the predictions shown, the height of mung beans will continue growing till the 16th day, and then it will decrease. In the real life, this prediction is unreasonable. It is impossible for plants to grow lower and lower as time passes. Therefore, It proves that the domain is correct, which is xϵ(0, 16.7198 ) when y is maximized.

Days Height (cm)

1 13

2 19

3 23

4 25

5 25

6 26

7 26.5

8 26.5

9 26.5

10 27.5

With Fertilizer (Table)

Linear Regression

0 2 4 6 8 10 120

5

10

15

20

25

30

f(x) = 1.24848484848485 x + 16.9333333333333R² = 0.700402720010563

HeightLinear (Height)Linear (Height)

Quadratic Regression

0 2 4 6 8 10 120

5

10

15

20

25

30

f(x) = − 0.280303030303031 x² + 4.33181818181819 x + 10.7666666666667R² = 0.926355053806034

HeightPolynomial (Height)Polynomial (Height)

Cubic Regression

0 2 4 6 8 10 120

5

10

15

20

25

30

f(x) = 0.0627428127428127 x³ − 1.31555944055944 x² + 9.10654623154624 x + 5.38333333333331R² = 0.992583578367892

HeightPolynomial (Height)Polynomial (Height)

Quartic Regression

0 2 4 6 8 10 120

5

10

15

20

25

30

f(x) = − 0.0059731934731936 x⁴ + 0.194153069153072 x³ − 2.27724358974361 x² + 11.7347513597514 x + 3.33333333333327R² = 0.995784897745682

HeightPolynomial (Height)Polynomial (Height)

Exponential Regression

0 2 4 6 8 10 120

5

10

15

20

25

30

f(x) = 16.7013589480336 exp( 0.0605718189364812 x )R² = 0.62882041699912

HeightExponential (Height)Exponential (Height)

Logarithmic Regression

0 2 4 6 8 10 120

5

10

15

20

25

30

f(x) = 5.92468411077541 ln(x) + 14.8511126825703R² = 0.924562897624409

HeightLogarithmic (Height)Logarithmic (Height)

The best fit model

The quartic regression is a best fit model in this case as r² closest to 1.

Model R2

Linear 0.7004

Quadratic 0.9264

Cubic 0.9926

Quartic 0.9958

Exponential 0.8802

Logarithmic 0.9246

Best fit Quartic Regression

0 2 4 6 8 10 120

5

10

15

20

25

30

f(x) = − 0.00597319 x⁴ + 0.1941531 x³ − 2.2772436 x² + 11.734751 x + 3.3333333R² = 0.995784897745682

HeightPolynomial (Height)Polynomial (Height)

Y= -0.006x4+ 0.1942x³ – 2.2772x² + 11.735x + 3.3333

Properties of the Best fit Function

Domain : (0, 11.3554)

Range : (0, 27.5462)

X-intercept : (16.8444,0)

Y-intercept : (0, 3.3333)

Predictionsf(11)=27.5113

f(13)=26.3329

f(15)=18.6633

f(16)=10.3573

f(17)=-2.3039

f(20)=-79.2467

In the real life, this prediction is unreasonable. It is impossible for plants to grow lower and lower as time passes. Moreover, the height appears a negative value as the prediction of the growing situation in the 17th day, which is totally impossible.

Therefore, we restricted the domain to (0, 16.8444) in that the height will be zero at this x value. As a matter of fact, our broad beans were stopped growing on the 11th day and were dead on the 14th day.

Conclusion

Based on our analysis, the quartic regression is the best fit model for the growth of our mung beans with and without fertilizer.

In terms of the 10 days’ growing, the broad beans with fertilizer grew higher than those without fertilizer.

Theoretically, the broad beans should have continued growing. However, in the real case, they were stopped growing since the 11th day.

We planted a lot of mung beans this time whereby the height was hard to measure. Furthermore, the death of our broad beans was probably speeded up by the crowded mung beans. Next time, we’d better plant a few broad beans in the same pot.

Thank You